This work aims at the development of a versatile numerical procedure to be used in a combined experimental/numerical analysis of the stability of plane parallel flows. To this purpose, a finite element approximation of the Orr-Sommerfeld equation is obtained using the Galerkin method with Hermite cubics as trial/test functions. The ensuing well-conditioned eigenvalue problem is solved by means of a QR algorithm. Plane Poiseuille and Couette flows are considered as test cases: a number of results are presented and compared with those previously obtained with different techniques (finite differences and Galerkin with orthogonal functions). When extended to unbounded domains, the present method shows promise for the analysis of boundary layer flows.
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